In this section, we give a short review of the flipped \(SU(5)\)  model [1]} constructed within the free-fermionic formulation of four-dimensional (4d) heterotic strings [2]}. For convenience of the reader, we use the same notation as in the original paper [1]}.
The model is generated by a set of basis vectors of boundary conditions for all world-sheet fermions with an appropriate choice of mutual GSO projections, given for self-consistency in Appendix A. It is equivalent to a \(Z_2\times Z_2\)  asymmetric orbifold of a \(N=4\)  supersymmetric model with gauge group \(U(8)\times SO(2)^6\times SO(10)\times SO(6)\) , generated by the vectors \(\lbrace  S, 1, \zeta , \alpha , b_1+b_4, b_2+b_5\rbrace \) . The \(Z_2\times Z_2\)  operation defined by the vectors \(\lbrace  b_1,b_2\rbrace \)  breaks supersymmetry to \(N=1\) , \(U(8)\rightarrow U(5)\times U(1)^3\)  and \(SO(2)^6\rightarrow SO(2)\) .
